Some algebraic characterizations of \(F\)-frames (Q987185)

The paper provides a number of equivalent conditions for a completely regular frame to be an \(F\)-frame. In particular, it is shown that a completely regular frame \(L\) is an \(F\)-frame iff the ring \(\mathcal R L\) of continuous real-valued functions on \(L\) is a Bézout ring (Proposition 3.2). It is also shown that \(\mathcal R L\) is almost weak Baer iff \(L\) is a strongly zero-dimensional \(F\)-frame (Proposition 4.9).